A Philosophical Introduction To Higher Order Logics

Author : Andrew Bacon
Publisher : Taylor & Francis
Page : 483 pages
File Size : 55,6 Mb
Release : 2023-09-29
Category : Philosophy
ISBN : 9781000925753

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A Philosophical Introduction to Higher-order Logics by Andrew Bacon Pdf

This is the first comprehensive textbook on higher-order logic that is written specifically to introduce the subject matter to graduate students in philosophy. The book covers both the formal aspects of higher-order languages—their model theory and proof theory, the theory of λ-abstraction and its generalizations—and their philosophical applications, especially to the topics of modality and propositional granularity. The book has a strong focus on non-extensional higher-order logics, making it more appropriate for foundational metaphysics than other introductions to the subject from computer science, mathematics, and linguistics. A Philosophical Introduction to Higher-order Logics assumes only that readers have a basic knowledge of first-order logic. With an emphasis on exercises, it can be used as a textbook though is also ideal for self-study. Author Andrew Bacon organizes the book's 18 chapters around four main parts: I. Typed Language II. Higher-Order Languages III. General Higher-Order Languages IV. Higher-Order Model Theory In addition, two appendices cover the Curry-Howard isomorphism and its applications for modeling propositional structure. Each chapter includes exercises that move from easier to more difficult, strategically placed throughout the chapter, and concludes with an annotated suggested reading list providing graduate students with most valuable additional resources. Key Features: Is the first comprehensive introduction to higher-order logic as a grounding for addressing problems in metaphysics Introduces the basic formal tools that are needed to theorize in, and model, higher-order languages Offers an abundance of - Simple exercises throughout the book, serving as comprehension checks on basic concepts and definitions - More difficult exercises designed to facilitate long-term learning Contains annotated sections on further reading, pointing the reader to related literature, learning resources, and historical context

Author : Stephen Pollard
Publisher : Courier Dover Publications
Page : 196 pages
File Size : 49,9 Mb
Release : 2015-07-15
Category : Mathematics
ISBN : 9780486797144

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Philosophical Introduction to Set Theory by Stephen Pollard Pdf

This unique approach maintains that set theory is the primary mechanism for ideological and theoretical unification in modern mathematics, and its technically informed discussion covers a variety of philosophical issues. 1990 edition.

Author : Jack Kaminsky,Alice R. Kaminsky
Publisher : Addison Wesley Publishing Company
Page : 360 pages
File Size : 45,9 Mb
Release : 1974
Category : Philosophy
ISBN : 0201035766

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Logic by Jack Kaminsky,Alice R. Kaminsky Pdf

Author : Nicholas Jones,Peter Fritz
Publisher : Oxford University Press
Page : 556 pages
File Size : 46,8 Mb
Release : 2024-06-21
Category : Philosophy
ISBN : 9780192894885

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Higher-Order Metaphysics by Nicholas Jones,Peter Fritz Pdf

This volume explores the use of higher-order logics in metaphysics. Seventeen original essays trace the development of higher-order metaphysics, discuss different ways in which higher-order languages and logics may be used, and consider their application to various central topics of metaphysics.

Author : William H. Brenner
Publisher : University of Notre Dame Pess
Page : 234 pages
File Size : 44,5 Mb
Release : 1993-09-30
Category : Philosophy
ISBN : 9780268158989

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Logic and Philosophy by William H. Brenner Pdf

The dual purpose of this volume—to provide a distinctively philosophical introduction to logic, as well as a logic-oriented approach to philosophy—makes this book a unique and worthwhile primary text for logic and/or philosophy courses. Logic and Philosophy covers a variety of elementary formal and informal types of reasoning, including a chapter on traditional logic that culminates in a treatment of Aristotle's philosophy of science; a truth-functional logic chapter that examines Wittgenstein's philosophy of language, logic, and mysticism; and sections on induction, analogy, and fallacies that incorporate material on mind-body dualism, pseudoscience, the "raven paradox," and proofs of God. Throughout the book Brenner highlights passages and ideas from various prominent philosophers, and discusses at some length the work of Plato, Aristotle, Descartes, Kant, and Wittgenstein.

Author : John Heil
Publisher : Hackett Publishing
Page : 303 pages
File Size : 41,8 Mb
Release : 2021-10-06
Category : Philosophy
ISBN : 9781647920104

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First-Order Logic by John Heil Pdf

"In his introduction to this most welcome republication (and second edition) of his logic text, Heil clarifies his aim in writing and revising this book: 'I believe that anyone unfamiliar with the subject who set out to learn formal logic could do so relying solely on [this] book. That, in any case, is what I set out to create in writing An Introduction to First-Order Logic.' Heil has certainly accomplished this with perhaps the most explanatorily thorough and pedagogically rich text I’ve personally come across. "Heil's text stands out as being remarkably careful in its presentation and illuminating in its explanations—especially given its relatively short length when compared to the average logic textbook. It hits all of the necessary material that must be covered in an introductory deductive logic course, and then some. It also takes occasional excursions into side topics, successfully whetting the reader’s appetite for more advanced studies in logic. "The book is clearly written by an expert who has put in the effort for his readers, bothering at every step to see the point and then explain it clearly to his readers. Heil has found some very clever, original ways to introduce, motivate, and otherwise teach this material. The author's own special expertise and perspective—especially when it comes to tying philosophy of mind, linguistics, and philosophy of language into the lessons of logic—make for a creative and fresh take on basic logic. With its unique presentation and illuminating explanations, this book comes about as close as a text can come to imitating the learning environment of an actual classroom. Indeed, working through its presentations carefully, the reader feels as though he or she has just attended an illuminating lecture on the relevant topics!" —Jonah Schupbach, University of Utah

Author : Timothy Williamson
Publisher : Oxford University Press
Page : 481 pages
File Size : 51,5 Mb
Release : 2013-03-28
Category : Philosophy
ISBN : 9780199552078

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Modal Logic as Metaphysics by Timothy Williamson Pdf

Timothy Williamson gives an original and provocative treatment of deep metaphysical questions about existence, contingency, and change, using the latest resources of quantified modal logic. Contrary to the widespread assumption that logic and metaphysics are disjoint, he argues that modal logic provides a structural core for metaphysics.

Author : John MacFarlane
Publisher : Routledge
Page : 256 pages
File Size : 53,6 Mb
Release : 2020-11-29
Category : Philosophy
ISBN : 9781351733557

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Philosophical Logic by John MacFarlane Pdf

Introductory logic is generally taught as a straightforward technical discipline. In this book, John MacFarlane helps the reader think about the limitations of, presuppositions of, and alternatives to classical first-order predicate logic, making this an ideal introduction to philosophical logic for any student who already has completed an introductory logic course. The book explores the following questions. Are there quantificational idioms that cannot be expressed with the familiar universal and existential quantifiers? How can logic be extended to capture modal notions like necessity and obligation? Does the material conditional adequately capture the meaning of 'if'—and if not, what are the alternatives? Should logical consequence be understood in terms of models or in terms of proofs? Can one intelligibly question the validity of basic logical principles like Modus Ponens or Double Negation Elimination? Is the fact that classical logic validates the inference from a contradiction to anything a flaw, and if so, how can logic be modified to repair it? How, exactly, is logic related to reasoning? Must classical logic be revised in order to be applied to vague language, and if so how? Each chapter is organized around suggested readings and includes exercises designed to deepen the reader's understanding. Key Features: An integrated treatment of the technical and philosophical issues comprising philosophical logic Designed to serve students taking only one course in logic beyond the introductory level Provides tools and concepts necessary to understand work in many areas of analytic philosophy Includes exercises, suggested readings, and suggestions for further exploration in each chapter

Author : Stewart Shapiro
Publisher : Routledge
Page : 352 pages
File Size : 50,9 Mb
Release : 2016-12-05
Category : Philosophy
ISBN : 9781351886666

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The Limits of Logic by Stewart Shapiro Pdf

The International research Library of Philosophy collects in book form a wide range of important and influential essays in philosophy, drawn predominantly from English-language journals. Each volume in the library deals with a field of enquiry which has received significant attention in philosophy in the last 25 years and is edited by a philosopher noted in that field.

Author : Stewart Shapiro
Publisher : Oxford University Press
Page : 856 pages
File Size : 42,9 Mb
Release : 2005-02-10
Category : Mathematics
ISBN : 9780190287535

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The Oxford Handbook of Philosophy of Mathematics and Logic by Stewart Shapiro Pdf

Mathematics and logic have been central topics of concern since the dawn of philosophy. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general philosophical issues and for its role in overall knowledge- gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on these topics in the best mainstream philosophical journals; in fact, the last decade has seen an explosion of scholarly work in these areas. This volume covers these disciplines in a comprehensive and accessible manner, giving the reader an overview of the major problems, positions, and battle lines. The 26 contributed chapters are by established experts in the field, and their articles contain both exposition and criticism as well as substantial development of their own positions. The essays, which are substantially self-contained, serve both to introduce the reader to the subject and to engage in it at its frontiers. Certain major positions are represented by two chapters--one supportive and one critical. The Oxford Handbook of Philosophy of Math and Logic is a ground-breaking reference like no other in its field. It is a central resource to those wishing to learn about the philosophy of mathematics and the philosophy of logic, or some aspect thereof, and to those who actively engage in the discipline, from advanced undergraduates to professional philosophers, mathematicians, and historians.

Author : Peter Fritz
Publisher : Cambridge University Press
Page : 137 pages
File Size : 48,9 Mb
Release : 2024-05-16
Category : Philosophy
ISBN : 9781009188630

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Propositional Quantifiers by Peter Fritz Pdf

Propositional quantifiers are quantifiers binding proposition letters, understood as variables. This Element introduces propositional quantifiers and explains why they are especially interesting in the context of propositional modal logics. It surveys the main results on propositionally quantified modal logics which have been obtained in the literature, presents a number of open questions, and provides examples of applications of such logics to philosophical problems.

Author : Paul Herrick
Publisher : Houghton Mifflin Harcourt P
Page : 600 pages
File Size : 51,5 Mb
Release : 1994
Category : Mathematics
ISBN : 0155003585

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The Many Worlds of Logic by Paul Herrick Pdf

Author : Robert Trueman
Publisher : Cambridge University Press
Page : 241 pages
File Size : 44,9 Mb
Release : 2021-01-07
Category : Philosophy
ISBN : 9781108890168

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Properties and Propositions by Robert Trueman Pdf

This book articulates and defends Fregean realism, a theory of properties based on Frege's insight that properties are not objects, but rather the satisfaction conditions of predicates. Robert Trueman argues that this approach is the key not only to dissolving a host of longstanding metaphysical puzzles, such as Bradley's Regress and the Problem of Universals, but also to understanding the relationship between states of affairs, propositions, and the truth conditions of sentences. Fregean realism, Trueman suggests, ultimately leads to a version of the identity theory of truth, the theory that true propositions are identical to obtaining states of affairs. In other words, the identity theory collapses the gap between mind and world. This book will be of interest to anyone working in logic, metaphysics, the philosophy of language or the philosophy of mind.

Author : Stewart Shapiro
Publisher : Clarendon Press
Page : 302 pages
File Size : 46,8 Mb
Release : 1991-09-19
Category : Mathematics
ISBN : 9780191524011

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Foundations without Foundationalism by Stewart Shapiro Pdf

The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to develop the argument fully, the author presents a detailed development of higher-order logic, including a comprehensive discussion of its semantics. Professor Shapiro demonstrates the prevalence of second-order notions in mathematics is practised, and also the extent to which mathematical concepts can be formulated in second-order languages . He shows how first-order languages are insufficient to codify many concepts in contemporary mathematics, and thus that higher-order logic is needed to fully reflect current mathematics. Throughout, the emphasis is on discussing the philosophical and historical issues associated with this subject, and the implications that they have for foundational studies. For the most part, the author assumes little more than a familiarity with logic as might be gained from a beginning graduate course which includes the incompleteness of arithmetic and the Lowenheim-Skolem theorems. All those concerned with the foundations of mathematics will find this a thought-provoking discussion of some of the central issues in this subject.

Author : Hans Bernhard Schmid
Publisher : Springer Science & Business Media
Page : 274 pages
File Size : 40,8 Mb
Release : 2009-05-30
Category : Philosophy
ISBN : 9789048124374

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Plural Action by Hans Bernhard Schmid Pdf

Collective Intentionality is a relatively new label for a basic social fact: the sharing of attitudes such as intentions, beliefs and emotions. This volume contributes to current research on collective intentionality by pursuing three aims. First, some of the main conceptual problems in the received literature are introduced, and a number of new insights into basic questions in the philosophy of collective intentionality are developed (part 1). Second, examples are given for the use of the analysis of collective intentionality in the theory and philosophy of the social sciences (part 2). Third, it is shown that this line of research opens up new perspectives on classical topics in the history of social philosophy and social science, and that, conversely, an inquiry into the history of ideas can lead to further refinement of our conceptual tools in the analysis of collective intentionality (part 3).